If you use the Apple Charging Case (only for standard not plus models), your phone will charge from the battery pack while using the Lightening EarPods.

Unless you have the Apple case or another 3rd party case with an external lightning connector with a battery that permits the battery to charge the phone -- you will not be able to charge the phone with these EarPods plugged in.

I like to listen to music while working. Sometimes there's training videos I need to watch at my desk as well. I don't want to disturb those around me, so I use headphones... actually, the same earbuds that I use with my iPhone because they're what I have on me and it's really convenient.

The audio signal through the lightning port will be digital not analog like the old 3.5mm jack's analog stereo signal. This should result in enhanced sound quality. However, not many people can hear a significant difference through Apple's lightning headphones.

It would be like connecting an iPhone to an external digital amplifier via the lightning port; Digital to digital suffers no sound depreciation unlike an analogue signal through a stereo jack. The sound quality of the digital signal is then determined by the quality of the amplification, speakers or headphones, not the signal itself.